The electron is not a classical object, so you can not talk of it's "motion" in a classical sense.

Quantum Leap (a term I'm coming across for the first time, in this context) is very different from Tunneling.

Your "Quantum Leap" is merely a consequence of energy conservation. You have an electron with a certain energy; you excite it (add energy to it), and as a result it now has a higher energy (or is in a higher energy state). This behavior is perfectly normal and there's nothing "forbidden" about it.

Quantum Tunneling is what happens when an electron with classically insufficient energy, crosses an energy barrier, (thanks to the "wackiness" of Quantum Mechanics).

Your "Quantum Leap" is merely a consequence of energy conservation. You have an electron with a certain energy; you excite it (add energy to it), and as a result it now has a higher energy (or is in a higher energy state). This behavior is perfectly normal and there's nothing "forbidden" about it.

From I've learnt in high school chemistry, electrons occupy different energy levels and located in specific orbitals or subshells s, p, d, and f where each orbitals vary in energy states.

We know from conservation of energy, energy taken by electrons can be written as

[tex]E=hc(\frac{1}{S^2}-\frac{1}{L^2}). [/tex]

As the formula says it, the energy of the photon equals the difference in energy between two energy levels which I believe is the difference between the different orbitals.

My real problem is with the rate at which the energy is converted, for electron at an energy level, according to Bohr, can only exist such that

[tex]E=-\frac{hcR}{n^2}[/tex]

So, if the above conditions are to be satisfied, wouldn't the rate of energy conversion be instantaneous thus violating Einstein's theory of relativity?

For large quantum numbers, the correspondence principle works. A transition [tex]n_m \rightarrow n_{m-1}[/tex] emits a photon with energy [tex]\hbar \omega[/tex]. This frequency omega is equal to the orbital frequency of the orbit in a classical model, which would emit dipole radiation with that orbital frequency. The energy loss would lead to the electron spiraling inwards, emitting radiation with increasing frequencies.